Photos of the tile floor in question

Paint or stencil is unlikely to work. You can probably put vinyl tile or sheets right over the tile.

"You can probably put vinyl tile or sheets right over the tile."

Yo can but you would absolutely need to fill in the grout joints or you will have telegraphing showing thru in short order.

Would steam cleaning help?

When I had a bad bathroom floor and was on a budget, I bought a carpet remnant and had the carpet co. come and cut to fit bath exactly. (Not a normal wall-to-wall installation, just lying flat. It didn't curl since it was regular carpeting with a rigid back.) It looked nice. Toilet ”overspray” wasnt an issue. ”cut to fit carpeting” used to be sold, maybe not now .

you dont have much to lose by painting using appropriate floor paint. Proper prep would be important. put diwn a pretty throw rug to prevent wear if bath is heavily used.